Homotopy in statistical physics

In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction to the mathematical methods involved in topology and homotopy theory, the role of the latter in a number of mainly low-dimensional statistical-mechanical systems is outlined. Some recent activities in this area are reviewed and some possible future directions are discussed.Comment: Significant extensions and updates: 29 pages, 11 figures. Lecture given at the Mochima Spring School, Mochima, Venezuela, June 2006. To appear in Cond. Matt. Phy

Statistical Physics in Meteorology

Various aspects of modern statistical physics and meteorology can be tied together. The historical importance of the University of Wroclaw in the field of meteorology is first pointed out. Next, some basic difference about time and space scales between meteorology and climatology is outlined. The nature and role of clouds both from a geometric and thermal point of view are recalled. Recent studies of scaling laws for atmospheric variables are mentioned, like studies on cirrus ice content, brightness temperature, liquid water path fluctuations, cloud base height fluctuations, .... Technical time series analysis approaches based on modern statistical physics considerations are outlined.Comment: Short version of an invited paper at the XXIth Max Born symposium,Ladek Zdroj, Poland; Sept. 200

Information in statistical physics

We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and theoretical reasons, and a probabilistic description involving the observers is required. The criterion of maximum von Neumann entropy is then used for making reasonable inferences. It means that no spurious information is introduced besides the known data. Its outcomes can be given a direct justification based on the principle of indifference of Laplace. We introduce the concept of relevant entropy associated with some set of relevant variables; it characterizes the information that is missing at the microscopic level when only these variables are known. For equilibrium problems, the relevant variables are the conserved ones, and the Second Law is recovered as a second step of the inference process. For non-equilibrium problems, the increase of the relevant entropy expresses an irretrievable loss of information from the relevant variables towards the irrelevant ones. Two examples illustrate the flexibility of the choice of relevant variables and the multiplicity of the associated entropies: the thermodynamic entropy (satisfying the Clausius-Duhem inequality) and the Boltzmann entropy (satisfying the H-theorem). The identification of entropy with missing information is also supported by the paradox of Maxwell's demon. Spin-echo experiments show that irreversibility itself is not an absolute concept: use of hidden information may overcome the arrow of time.Comment: latex InfoStatPhys-unix.tex, 3 files, 2 figures, 32 pages http://www-spht.cea.fr/articles/T04/18

Statistical Physics of Structural Glasses

This paper gives an introduction and brief overview of some of our recent work on the equilibrium thermodynamics of glasses. We have focused onto first principle computations in simple fragile glasses, starting from the two body interatomic potential. A replica formulation translates this problem into that of a gas of interacting molecules, each molecule being built of $m$ atoms, and having a gyration radius (related to the cage size) which vanishes at zero temperature. We use a small cage expansion, valid at low temperatures, which allows to compute the cage size, the specific heat (which follows the Dulong and Petit law), and the configurational entropy. The no-replica interpretation of the computations is also briefly described. The results, particularly those concerning the Kauzmann tempaerature and the configurational entropy, are compared to recent numerical simulations.Comment: 21 pages, 6 figures, to appear in the proceedings of the Trieste workshop on "Unifying Concepts in Glass Physics

Statistical Physics of Self-Replication

Self-replication is a capacity common to every species of living thing, and simple physical intuition dictates that such a process must invariably be fueled by the production of entropy. Here, we undertake to make this intuition rigorous and quantitative by deriving a lower bound for the amount of heat that is produced during a process of self-replication in a system coupled to a thermal bath. We find that the minimum value for the physically allowed rate of heat production is determined by the growth rate, internal entropy, and durability of the replicator, and we discuss the implications of this finding for bacterial cell division, as well as for the pre-biotic emergence of self-replicating nucleic acids.Comment: 4+ pages, 1 figur

Statistical Physics of RNA-folding

We discuss the physics of RNA as described by its secondary structure. We examine the static properties of a homogeneous RNA-model that includes pairing and base stacking energies as well as entropic costs for internal loops. For large enough costs the model exhibits a thermal denaturation transition which we analyze in terms of the radius of gyration. We point out an inconsistency in the standard approach to RNA secondary structure prediction for large molecules. Under an external force a second order phase transition between a globular and an extended phase takes place. A Harris-type criterion shows that sequence disorder does not affect the correlation length exponent while the other critical exponents are modified in the glass phase. However, at high temperatures, on a coarse-grained level, disordered RNA is well described by a homogeneous model. The characteristics of force-extension curves are discussed as a function of the energy parameters. We show that the force transition is always second order. A re-entrance phenomenon relevant for real disordered RNA is predicted.Comment: accepted for publication in Phys. Rev.

Statistical physics for cosmic structures

The recent observations of galaxy and dark matter clumpy distributions have provided new elements to the understating of the problem of cosmological structure formation. The strong clumpiness characterizing galaxy structures seems to be present in the overall mass distribution and its relation to the highly isotropic Cosmic Microwave Background Radiation represents a fundamental problem. The extension of structures, the formation of power-law correlations characterizing the strongly clustered regime and the relation between dark and visible matter are the key problems both from an observational and a theoretical point of view. We discuss recent progresses in the studies of structure formation by using concepts and methods of statistical physics.Comment: 8 pages, 4 figures, European Physical Journal B - STATPHYS 23 topical issue in the press (2007